Here, I report on a cryogenic cavity optomechanics experiment that has been set up with the goal to cool a mechanical degree of freedom of a fused silica microtoroidal resonator into the quantum regime by means of a combination of cryogenic and laser cooling. Based on the experience with a Helium-4 exchange gas cryostat obtained during a previous cryogenic optomechanics experiment, a novel setup with a Helium-3 cryostat at its heart has been set up. Cooling of a mechanical degree of freedom of a microtoroid close to its motional quantum ground state could be achieved and a regime, where full quantum control becomes possible, has come into reach. Silica microtoroids sustain at the same time ultra-high finesse optical whispering gallery modes (WGM) as well as radial mechanical modes ("radial breathing modes", RBM). The two degrees of freedom are mutually coupled, since mechanical motion changes the optical resonance frequency, and the mechanical motion is affected by the radiation pressure forces of an optical field contained in the optical mode. As the optical cavity lifetime is finite, the intracavity optical field amplitude is not adjusting instantaneously to the changed boundary conditions as induced by a mechanical displacement, but in a retarded manner, which gives rise to an effect known as dynamical backaction, that for example can be used to laser cool a mechanical mode. Using a 1550 nm laser important insight has been gained on the dependency of mechanical decay rate and frequency as a function of temperature, which is dominated by two level systems within amorphous fused silica. The different temperature regimes have been explored, including experiments at the lowest accessible temperatures, where evidence of resonant saturable absorption of TLS has been found. Using 780 nm light instead, cooling below ten quanta could be achieved and "optomechanically induced transparency", the optomechanical equivalent of electromagnetically induced transparency as found in atomic vapors, could be demonstrated, enabling all-optical switching of a laser beam and storage of pulses. Novel, optimized spokes-supported toroids then enabled us to push up the optomechanical coupling sufficiently, such that cooling to below two thermal quanta could be achieved and —for the first time in the optical domain— the quantum-coherent coupling regime could be accessed. Here, the optomechanical coupling rate exceeds the optical and mechanical decay rates (i.e. "strong coupling"), but also the mechanical decoherence rate, such that quantum-state transfer between optics and mechanics comes into reach. In addition, this thesis contains the technological steps taken and experimental hurdles overcome towards these experiments.